The length of latus rectum of the conic passing through the origin and having the property that normal at each point (x$$, $$y) intersects the $$x-axis$$ at $$x+1$$,$$0$$ is:

Question

The length of latus rectum of the conic passing through the origin and having the property that normal at each point (x$$, $$y) intersects the $$x-axis$$ at  $$x+1$$,$$0$$ is:

Infinity Learn · Accepted Answer

Let px,y  be any point on the conic. ∴ slope of normal $$l=$$−dxdyEquation of normal to conic at px,y is Y−$$y=$$−dxdyX−x⇒−$$y=$$−dxdyX−x     (on$$ $$x-axis$$ Y $$=$$ $$0)⇒$$X=x+ydydx$$  Given  $$X=x+1$$  ⇒  $$ydydx=1ydy=dx$$⇒$$y22=x+C$$.......i   Since the conic passes through origin, x $$=$$ $$0$$, y $$=$$ $$0$$ in (i) we get C $$=$$ $$0$$∴ From  (i)  $$y2=2x$$ Which is parabola having length of latus rectum  $$=$$ $$4a=2units$$

The length of latus rectum of the conic passing through the origin and having the property that normal at each point (x, y) intersects the x-axis at $((x + 1), 0)$ is:

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The length of latus rectum of the conic passing through the origin and having the property that normal at each point (x, y) intersects the x-axis at x+1,0 is:

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The length of latus rectum of the conic passing through the origin and having the property that normal at each point (x, y) intersects the x-axis at $((x + 1), 0)$ is: